document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42842>Question 42842</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am working on factoring trinomials. The thing is I am so confused with some problems. \r<BR>\n" );
document.write( "\n" );
document.write( "2x² + x - 6\r<BR>\n" );
document.write( "\n" );
document.write( "can you help me???? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27904 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1806)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><font size = 5><b>\r\n" );
document.write( "I am working on factoring trinomials. The thing is \r\n" );
document.write( "I am so confused with some problems. \r\n" );
document.write( "\r\n" );
document.write( "                   2x² + x - 6\r\n" );
document.write( "\r\n" );
document.write( "can you help me????\r\n" );
document.write( "\r\n" );
document.write( "-------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "To factor Ax² ± Bx ± C when there is no common factor \r\n" );
document.write( "of |A|, |B|, and |C| and A is positive.\r\n" );
document.write( "\r\n" );
document.write( "1. Multiply |A| by |C|, getting AC\r\n" );
document.write( "\r\n" );
document.write( "2. If the last sign is +, think of two positive integers\r\n" );
document.write( "   which have product AC and which have SUM |B|\r\n" );
document.write( "   If the last sign is -, think of two positive integers \r\n" );
document.write( "   which have product AC and which have DIFFERENCE |B|\r\n" );
document.write( "\r\n" );
document.write( "3. Rewrite the middle term ±Bx using those two integers \r\n" );
document.write( "   found in the preceding step, attaching appropriate\r\n" );
document.write( "   signs.\r\n" );
document.write( "\r\n" );
document.write( "4. Factor by grouping.  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In your problem, 2x² + 1x - 6, I placed the 1 coefficient\r\n" );
document.write( "beside the middle term for emphasis.\r\n" );
document.write( "\r\n" );
document.write( "1. Multiply |A| by |C|, getting AC\r\n" );
document.write( "\r\n" );
document.write( "   Multiply |2| by |-6| or 2×6 getting 12\r\n" );
document.write( "\r\n" );
document.write( "2. The last sign is -, so think of two positive integers \r\n" );
document.write( "   which have product AC and which have DIFFERENCE |B|\r\n" );
document.write( "\r\n" );
document.write( "   So we think of two positive integers which have product\r\n" );
document.write( "   12 and difference of 1.  These are 4 and 3, because\r\n" );
document.write( "   4×3=12 and 4-3 = 1 \r\n" );
document.write( "\r\n" );
document.write( "3. Rewrite the middle term ±Bx using those two integers \r\n" );
document.write( "   found in the preceding step, attaching appropriate \\r\n" );
document.write( "   signs.\r\n" );
document.write( "\r\n" );
document.write( "   We rewrite +1x as +4x - 3x.  So now we have\r\n" );
document.write( "\r\n" );
document.write( "   2x² + 4x - 3x - 6\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "4. Factor by grouping.\r\n" );
document.write( "\r\n" );
document.write( "   2x² + 4x - 3x - 6\r\n" );
document.write( "\r\n" );
document.write( "Factor 2x out of the first two terms\r\n" );
document.write( "\r\n" );
document.write( "  2x(x + 2) - 3x - 6\r\n" );
document.write( "\r\n" );
document.write( "Factor -3 out of the last two terms.  Notice\r\n" );
document.write( "that you factor out a negative when the next\r\n" );
document.write( "to the last term is preceded by a minus sign.\r\n" );
document.write( "Also when factoring out a nagative, the sign\r\n" );
document.write( "of the last term changes:\r\n" );
document.write( "\r\n" );
document.write( " 2x(x + 2) - 3(x + 2)\r\n" );
document.write( "\r\n" );
document.write( "Notice the common factor (x + 2) which I will\r\n" );
document.write( "color red for emphasis:\r\n" );
document.write( "\r\n" );
document.write( " 2x<font color = \"red\">(x + 2)</font> - 3<font color = \"red\">(x + 2)</font>\r\n" );
document.write( "   \r\n" );
document.write( "We factor out the common red factor and leave \r\n" );
document.write( "the black factors inside parentheses:\r\n" );
document.write( "\r\n" );
document.write( "  <font color = \"red\">(x + 2)</font>(2x - 3)\r\n" );
document.write( "\r\n" );
document.write( "  (x + 2)(2x - 3)\r\n" );
document.write( "\r\n" );
document.write( "--------------------------\r\n" );
document.write( "\r\n" );
document.write( "Here is another example:\r\n" );
document.write( "\r\n" );
document.write( "Factor  6x² - 19x + 10.\r\n" );
document.write( "\r\n" );
document.write( "1. Multiply |A| by |C|, getting AC\r\n" );
document.write( "\r\n" );
document.write( "   Multiply |6| by |10| or 6×10 getting 60\r\n" );
document.write( "\r\n" );
document.write( "2. The last sign is +, so think of two positive integers \r\n" );
document.write( "   which have product AC and which have SUM |B|\r\n" );
document.write( "\r\n" );
document.write( "   So we think of two positive integers which have product\r\n" );
document.write( "   60 and sum of 19.  These are 15 and 4, because\r\n" );
document.write( "   15×4=60 and 15+4 = 19  \r\n" );
document.write( "\r\n" );
document.write( "3. Rewrite the middle term ±Bx using those two integers \r\n" );
document.write( "   found in the preceding step, attaching appropriate signs.\r\n" );
document.write( "\r\n" );
document.write( "   We rewrite -19x as -15x - 4x.  So now we have\r\n" );
document.write( "\r\n" );
document.write( "   6x² - 15x - 4x + 10\r\n" );
document.write( "\r\n" );
document.write( "4. Factor by grouping.\r\n" );
document.write( "\r\n" );
document.write( "   6x² - 15x - 4x + 10\r\n" );
document.write( "\r\n" );
document.write( "Factor 3x out of the first two terms\r\n" );
document.write( "\r\n" );
document.write( "  3x(2x - 5) - 4x + 10\r\n" );
document.write( "\r\n" );
document.write( "Factor -2 out of the last two terms.  Notice\r\n" );
document.write( "that you factor out a negative when the next\r\n" );
document.write( "to the last term is preceded by a minus sign.\r\n" );
document.write( "Also when factoring out a nagative, the sign\r\n" );
document.write( "of the last term changes:\r\n" );
document.write( "\r\n" );
document.write( " 3x(2x - 5) - 2(2x - 5)\r\n" );
document.write( "\r\n" );
document.write( "Notice the common factor (2x - 5) which I will\r\n" );
document.write( "color red for emphasis:\r\n" );
document.write( "\r\n" );
document.write( " 3x<font color = \"red\">(2x - 5)</font> - 2<font color = \"red\">(2x - 5)</font>\r\n" );
document.write( "   \r\n" );
document.write( "We factor out the common red factor and leave \r\n" );
document.write( "the black factors inside parentheses:\r\n" );
document.write( "\r\n" );
document.write( "  <font color = \"red\">(2x - 5)</font>(3x - 2)\r\n" );
document.write( "\r\n" );
document.write( "  (2x - 5)(3x - 2)\r\n" );
document.write( "\r\n" );
document.write( "Edwin</PRE>  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );